CN105519030A - Device and computer program product for fast link adaptation in communication system - Google Patents

Abstract

A transceiver for selecting channel state information for fast link adaptation in a communication system. The transceiver includes a radio frequency unit and a memory coupled to a processing device. The processing device is used for: generating channel and noise covariance estimation values and cyclic redundancy check results based on the received data signals; generating a set of Link Quality Metrics (LQM) based on the estimate; caching the generated set of LQMs; updating model parameters using a Gaussian Process (GP) system model based on the cached set of LQMs and the set of CRC results; predicting a block error rate (BLER) for each CSI in the supported set of CSI using the updated model parameters and the GP system model based on the generated set of LQMs; selecting the CSI with the largest throughput and a predicted BLER below a threshold from the supported set of CSIs.

Description

Device and computer program product for fast link adaptation in communication system

technical field

Aspects of the invention relate generally to communication systems employing link feedback, and more particularly to fast link adaptation techniques.

Background technique

With the ubiquity of modern wireless communication devices such as mobile phones, smartphones and tablet devices, there is also the need for massive multimedia data capabilities such as streaming video, TV, music and Internet access for user equipment (UE) or mobile station (MS) surge. To meet this growing demand for higher data rates, new communication standards based on techniques such as Multiple Input Multiple Output (MIMO), Orthogonal Frequency Division Multiple Access (OFDMA), and Bit Interleaved Coded Modulation (BICM) Developing. Examples of these standards include Long Term Evolution (LTE) and LTE-Advanced (LTE-A) being developed by the Third Generation Partnership Project (3GPP), the 802.11 and 802.16 series of wireless broadband standards maintained by the Institute of Electrical and Electronics Engineers (IEEE), WiMAX Forum's implementation of the IEEE802.11 standard, WiMAX, and other standards.

The quality of data transmitted over wireless communication channels is often complicated by the volatility of the medium, affected by factors such as fading, interference from other users, and variations between UE devices. Adapting system parameters such as modulation coding scheme (MCS) or transmit power according to current channel conditions is known to significantly improve overall throughput. However, to adapt a communication link or a link between a transmitter and a receiver, the transmitter needs accurate knowledge of the current channel state information (CSI) of the link.

To accommodate this, modern communication systems such as those described above include some type of feedback mechanism to allow closed-loop adaptation of the link between the transmitter, which may be located at a base transceiver station or eNodeB, and the receiver at the on MS or UE. For example, the 3GPP LTE and LTE-A standards include provisions for sending CSI from a UE or MS back to the transmitter, where the CSI is used to select the modulation coding scheme (MCS), and/or precoding matrix, and/or rank number, etc. for transmission parameter. LTE includes several types of CSI, including Channel Quality Indication (CQI), Rank Indication (RI), and Precoding Matrix Indication (PMI). The CQI is an integer value between 1 and 15. Generally speaking, each CQI value corresponds to one of 29 MCSs, and these 29 MCSs are used for data transmission on the physical downlink shared channel (PDSCH) excluding HARQ retransmission. In this scheme, a higher CQI value corresponds to a higher throughput MCS. Hereafter, CQI and MCS are used interchangeably.

The process of determining the appropriate CSI value for the receiver, sending the CSI to the transmitter, and modifying the link based on the received CSI is called Link Adaptation (LA), and is usually used in systems using MIMO-OFDMA technology In, for example, the PDSCH defined in 3GPP LTE Rel-8. The purpose of LA is to adjust transmission parameters such as MCS and/or precoding matrix and/or rank number such that the block error rate (BLER), a typical quality of service QoS metric used in wireless and other communication systems, is kept below the given Maximize the average throughput of the physical layer while setting the threshold. The BLER threshold used in mobile communication systems is usually about 0.1, or 10%, and can be adjusted up or down according to the desired QoS.

In mobile communication systems, link adaptation schemes are usually used to implement transmissions from a radio base station to MSs, called downlink (DL), but can also be used to improve uplink (UL) transmissions. To implement LA, a receiver receives transmission data comprising packets and computes a link quality metric (LQM) based on the received signal. The receiver then determines appropriate CSI values and sends them to the transmitter, where these CSI values are used to select link parameters for subsequent data transmissions. The wireless link is a very unstable medium, so when a CSI value is calculated and sent to the transmitter to adjust the link parameters, the link may have changed greatly, resulting in the failure of the self-adaptation to achieve the desired effect. Therefore, when using the modified transmission scheme, the receiver should try to predict the future CSI instead of just calculating the current CSI value and returning it to the transmitter, so as to improve the link throughput. Therefore, LA needs to predict the best CSI for next transmission according to current and past channel information. Since wireless links are constantly and rapidly changing, the LA algorithm used for CSI prediction must adjust fast enough to keep track of these changes. An algorithm that can adapt to these rapid link changes is called Fast Link Adaptation (FLA).

FLA can be a tricky and challenging problem. In a harsh environment that is dynamic and subject to various changes, such as slow or fast fading scenarios, heterogeneous networks, interference and changes in UE conditions due to motion, temperature and inter-UE variation, the transmission parameters Tuning to maximize average throughput performance while maintaining an acceptably low BLER can be difficult. An ideal FLA technique should satisfy a number of constraints, including the following:

In order to maximize the average throughput while keeping the BLER below a given threshold, the FLA should be able to recommend an MCS/CQI suitable for any practical mobile environment;

The FLA technique should have a "fast" adaptation rate so it can closely track changes in channel quality;

The number of parameters and/or look-up tables (LUTs) must be kept small and the computational complexity must be kept constant under different channel conditions;

The FLA technique should be able to successfully cope with linear and nonlinear channel equalizers, knowledge of imperfect channels and noise covariance, and radio frequency (RF) imperfections.

Many solutions to the FLA problem have been proposed, each with its advantages and disadvantages. A classic approach is to use a link quality metric (LQM) with or without calibration and correction, such as Mean Mutual Information Per Coded Bitmap (MMIBM). In this approach, a scalar link quality metric (LQM) is obtained by utilizing a set of post-processing signal-to-interference-noise ratios (SINRs) of the employed equalizer. However, only linear minimum mean square error (LMMSE) type equalizers are aware of closed-form post-processing SINR. For other types of equalizers, such as maximum likelihood (ML) type equalizers, some approximation is required. After obtaining a scalar LQM such as MCS for each transmission parameter, the classic classical approach is to find the corresponding BLER from the LQM-to-BLER mapping, which is usually created offline. The off-line mapping or look-up table (LUT) is obtained by the MCS respectively under additive white Gaussian noise (AWGN) channel conditions, taking into account the transport block size. Thereafter, an appropriate spectrally efficient MCS scheme is recommended such that the predicted BLER of the considered MCS scheme is below the desired threshold. The predicted BLER threshold is obtained by simulation, so that the average BLER can meet the constraints of the desired QoS requirements. This "classical" approach has been empirically studied in the literature and shows good performance in a calibrated setting. Unfortunately, finding the calibration and correction factors for each required MCS and channel condition requires long and tedious simulations. Different transfer sizes require several LUTs, so this approach cannot be used for LTE/LTE-A based systems. It is also difficult to find a suitable correction factor when using a non-linear or ML type equalizer. In real systems, radio frequency (RF) imperfections are unavoidable and can negatively impact performance because correction factors cannot be adjusted to accommodate all types of real-world variations and imperfections.

The FLA technique based on Support Vector Machine (SVM) has also been established. These methods use SVM to learn the mapping between mean or ordered post-processing SINR and BLER for each candidate MCS in real-time or online. This learned map is regularly updated and used to predict the BLER performance of each set of supported MCS schemes. Then, the predicted BLER value can be used to select and recommend an MCS scheme for the next packet. SVM-based FLA outperforms classical LQM/LUT-based methods and can also cope with certain types of RF and nonlinear imperfections. However, SVM-based methods suffer from high memory consumption and insufficient complexity cost to be implemented in current state of the art digital signal processing (DSP) devices. How well SVM-based FLA techniques work in non-stationary scenarios or whether they can properly track system changes remains unknown.

Another LA solution is an online kernel method (OKM) called quantized kernel least mean square (QKLMS). QKLMS is similar to SVM methods in terms of learning the mapping between mean or ordered post-processed SINR and BLER, but QKLMS is less complex and has much lower memory requirements than currently known SVM methods. While QKLMS has some advantages, there are also some problems with this approach. QKLMS has poor tracking ability and is more accurately characterized as a "slow" LA technique. Finding QKLMS free hyperparameters via exhaustive and time-consuming offline grid search. Additional searches are required to determine how to select a suitable MCS from the set of available MCSs. The input to the OKM is the average post-processing SINR or a set of ordered post-processing SINRs in an equalizer, both of which have a very high dynamic range, thus reducing the potential gain provided by the OKM.

Therefore, it is desirable to find a FLA technique that can solve at least some of the above-mentioned problems.

Contents of the invention

Against the above technical background, it is an object of the present invention to provide a device and a method by which the data transmission rate in a communication link using link adaptive feedback can be increased, especially but not exclusively for the purpose at the receiver Select CSI.

Another object of the present invention is to provide devices and methods such that FLA can be used to adjust or recommend suitable CSI values in dynamic environments to maximize the average throughput of a communication link while keeping the average BLER below a desired threshold. These devices and methods provide a "fast" adaptation rate that closely tracks rapid changes in channel state.

Yet another object of the present invention is to provide apparatus and methods such that FLA can be used to keep the number of parameters and/or look-up tables (LUTs) small and keep constant computational complexity under different channel conditions.

Yet another object of the present invention is to provide apparatus and methods by which FLA can be used to successfully cope with linear and non-linear channel equalizers, imperfect channel and noise covariance knowledge, and radio frequency (RF) imperfections in stationary or non-stationary environments.

The above and further objects and advantages are all according to the present invention, by using a Gaussian Process (GP) system model, whose model parameters can be adjusted and updated to quickly track channel state changes of communication links. The updated GP system model is used to predict the BLER performance of future transmissions for a desired set of CSIs, selecting a CSI associated with the highest throughput and capable of maintaining the predicted BLER below a predetermined threshold.

According to a first aspect of the present invention, the above and further objects and advantages are obtained by a channel state information (CSI) transceiver operable to select a communication link. The transceiver includes: a receiver for receiving a communication signal from the communication link and generating a received data signal; processing means coupled to the receiver for receiving the data signal; A memory coupled to the processing device. The processing device is configured to: generate a channel estimate, a noise covariance estimate, and a set of cyclic redundancy check (CRC) results based on the received data signal; generate a channel estimate and a noise covariance estimate based on the channel estimate and the noise covariance estimate A set of link quality metrics (LQMs); buffering the generated set of LQMs. A Gaussian Process (GP) system model is used to update model parameters of a GP system model based on the cached set of LQMs and the set of CRC results. Based on the generated set of LQMs, the Block Error Rate (BLER) is predicted for each CSI in the supported set of CSIs using the updated model parameters and the GP system model. The processing means selects from the supported set of CSIs the CSI with the maximum throughput and a predicted BLER below a threshold.

According to the first aspect, in the first possible implementation form of the transceiver, using the GP system model to update the model parameters includes: based on the generated set of CRC results, the cached set of LQM and training Data dictionary, update model parameters. The training data dictionary is updated based on the cached set of LQMs, generated CRC results and the CSI of the received data signal.

According to the first possible implementation form of the first aspect, in the second possible implementation form of the transceiver, the training data dictionary includes multiple sets of cached LQMs, at least one set of LQMs associated with each set of LQMs CRC result, and an associated set of CSI.

According to the second possible implementation form of the first aspect, in the third possible implementation form of the transceiver, the training data dictionary is enhanced in the following manner: when the CRC result generated for the current CSI is passed, All low-throughput CSIs in the supported set of CSIs are associated with the CRC passing result; when the CRC generated for the current CSI fails, all high-throughput CSIs in the supported set of CSIs are associated with the CRC failure result association.

According to the first aspect or the first to third possible implementation forms of the first aspect, in a fourth possible implementation form of the transceiver, the GP system model is a non-recursive GP system model .

According to the first aspect or the first to third possible implementation forms of the first aspect, in a fifth possible implementation form of the transceiver, the GP system model is a recursive system model.

According to the first aspect or any one of the first to fifth possible implementation forms of the first aspect, in the sixth possible implementation form of the transceiver, the LQM209 is an effective The mean mutual information (mean MI) measure of .

According to the sixth possible implementation form of the first aspect, in the seventh possible implementation form of the transceiver, generating a set of average MIs includes: based on the assumption of a linear equalizer, and the received data signal After nonlinear equalization adjustment, a mutual information (MI) value is generated for each RE in the received data signal; based on the generated MI value, the set of effective average MI is generated.

According to the fourth or fifth possible implementation form of the first aspect, in the eighth possible implementation form of the transceiver, the GP system model includes a set of GP system models, and in the set of GP system models Each GP system model of is used to predict BLER for a particular CSI, when the CSI associated with the received data signal is not associated with any of the set of GP system models, the GP system model associated with the nearest CSI get updated.

According to the first aspect or any one of the first to eighth possible implementation forms of the above first aspect, in the ninth possible implementation form of the transceiver, the CSI value is a broadband Channel Quality Indicator (CQI), Subband CQI, Rank Indication, Wideband Precoding Matrix Indicator (PMI), or Subband PMI.

According to the first aspect or any one of the first to ninth possible implementation forms of the above first aspect, in the tenth possible implementation form of the transceiver, the communication link includes a wireless A communication link, the receiver including a radio frequency (RF) unit.

According to the first aspect or any one of the first to tenth possible implementation forms of the above first aspect, in the eleventh possible implementation form of the transceiver, the communication link includes Orthogonal Frequency Division Multiple Access (OFDMA) type communication link.

According to an eleventh possible form of the first aspect, in a twelfth possible implementation form of the transceiver, the system comprises nonlinear equalization or linear equalization.

According to the first aspect or any one of the tenth to the twelfth possible implementation forms of the first aspect, in the thirteenth possible implementation form of the transceiver, the system is a A user device, including user interface and display.

According to a second aspect of the present invention, the above and further objects and advantages are achieved by a computer program product comprising a non-transitory computer-readable storage medium storing data which, when accessed by a processing device, performs an operation , comprising: receiving channel estimate and noise covariance estimate; generating a set of link quality metrics (LQM) based on the channel estimate and noise covariance estimate; buffering the generated set of LQM; based on the received data signal, generating a set of cyclic redundancy check (CRC) results; based on the cached set of LQMs and the set of CRC results, using the Gaussian process (GP) system model to update the model parameters of the GP system model; based on the generated A set of LQMs, using the updated model parameters and the GP system model to predict a block error rate (BLER) for each CSI in the supported set of CSIs; selecting the CSI with the largest throughput from the supported set of CSIs and Predicted BLER below threshold.

According to a third aspect of the present invention, the above and further objects and advantages are obtained by a method based on selected channel state information (CSI) in a communication system. The method comprises: >receiving a channel estimate and a noise covariance estimate; generating a set of link quality metrics (LQM) based on the channel estimate and the noise covariance estimate. Cache the set of LQMs described. generating a set of cyclic redundancy check (CRC) results based on the received data signal; updating a set of model parameters using a Gaussian process (GP) system model based on the cached set of LQMs and the generated CRC results . The updated set of model parameters is used in the GP system model to predict a block error rate (BLER) for each CSI in a supported set of CSIs. Then, a CSI is selected from the supported set of CSIs, the selected CSI has the maximum throughput and the predicted BLER is lower than a predetermined threshold.

According to the third aspect, in the first possible implementation form of the method, using the GP system model to update the model parameters includes: based on the generated set of CRC results, the cached set of LQM and the training data dictionary , updating model parameters; updating the training data dictionary according to the cached set of LQMs, the generated CRC results, and the CSI of the received data signal.

According to the third aspect or the first possible implementation form of the third aspect, in the second possible implementation form of the method, the training data dictionary includes multiple sets of cached LQMs, and at least A set of CRC results, and an associated set of CSI.

According to the third aspect or the second possible implementation form of the third aspect, in the third possible implementation form of the method, the training data dictionary is enhanced; when the CRC result generated for the current CSI is passed, All low-throughput CSIs in the supported set of CSIs are associated with the CRC passing result; when the CRC result generated for the current CSI is passed, all low-throughput CSIs in the supported set of CSIs are associated with the CRC is correlated by result.

According to the third aspect or any one of the first to third possible implementation forms of the third aspect, in the fourth possible implementation form of the method, the GP system model is a non-recursive GP system model.

According to the third aspect or any one of the first to third possible implementation forms of the third aspect, in the fifth possible implementation form of the method, the GP system model is a recursive system Model.

According to the third aspect, the purpose of a fifth possible implementation of the method is to avoid the computational complexity associated with matrix inversions required for non-recursive GP system models.

According to the third aspect or any one of the first to fifth possible implementation forms of the third aspect, in the sixth possible implementation form of the method, the LQM is an effective average interaction Information (mean MI) measure.

According to the third aspect or the sixth possible implementation form of the third aspect, in the seventh possible implementation form of the method, generating a set of average MIs includes: based on the assumption of a linear equalizer, and receiving The data signal of the received data signal is adjusted by nonlinear equalization, and a set of mutual information (MI) values is generated for each RE in the received data signal; based on the generated set of MI values, the set of effective average MI is generated.

According to the third aspect or the fourth or fifth implementation form of the third aspect, in the eighth possible implementation form of the method, the GP system model includes a set of GP system models, and the set of GP system models Each GP system model in the model is used to predict the BLER for a particular CSI, when the CSI associated with the received data signal is not associated with any GP system model in the set of GP system models, the one associated with the nearest CSI The GP system model has been updated.

According to the third aspect or any one of the above-mentioned first to eighth implementation forms according to the third aspect, in a ninth possible implementation form of the method, the CSI value is a wideband channel quality indicator ( CQI), subband CQI, rank indication, wideband precoding matrix indication (PMI), or subband PMI.

These and other aspects, implementations and advantages of the exemplary embodiments are apparent from the following description of the embodiments in conjunction with the accompanying drawings. It should be understood, however, that such description and drawings are for illustrative purposes only and not as limitations of the invention; for any limitations on the invention, reference should be made to the appended claims. Additional aspects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Furthermore, the aspects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the appended claims.

Description of drawings

In the attached picture:

Figure 1 shows a block diagram of a simplified LTE receiver incorporating all aspects of the disclosed embodiments;

FIG. 2 shows a flowchart of an exemplary method for selecting channel state information that integrates all aspects of the disclosed embodiments;

Fig. 3 shows the training and prediction mode of the GP system model of wideband-CQI prediction integrated with all aspects of the disclosed embodiments;

Figure 4 shows a graph of the total throughput of the physical downlink shared channel integrating all aspects of the present invention;

Fig. 5 shows the average BLER graph of the physical downlink shared channel integrating all aspects of the present invention;

Figure 6 shows a graph illustrating the tracking performance of the LA technique incorporating all aspects of the present invention;

Figure 7 shows a block diagram of an apparatus suitable for FLA incorporating all aspects of the disclosed embodiments.

detailed description

The embodiments disclosed in the present invention avoid many problems in the prior art through the new technology of FLA. These new techniques are based on regression/classification methods using nonparametric Gaussian processes (GP) for online learning and BLER prediction. GP is a Bayesian approach to nonparametric regression and classification that is more in-principle than the prior art described above. And, in addition to providing a predicted mean estimate, GP-based techniques also provide an uncertainty in the estimate (unlike in OKM), which can be used to improve link adaptation. The disclosed GP-based FLA technique uses a probabilistic approach to solve challenging FLA problems, which has several advantages over state-of-the-art solutions while maintaining low complexity and low memory requirements. Some desirable properties of the disclosed GP-based FLA technique are listed below:

The disclosed GP-based FLA mechanism is capable of adjusting or recommending an appropriate CSI value in a dynamic environment to maximize average throughput and keep average BLER below a desired threshold;

The disclosed GP-based FLA technique works acceptable in both stationary and non-stationary environments;

The number of parameters is small;

Complexity remains constant and memory requirements are low;

The disclosed GP-based FLA technique can successfully cope with linear and nonlinear channel equalizers, imperfect channel state information, and RF imperfections.

The prior art OKM-LA system uses the post-processing SINR of the MIMO equalizer as the LQM and performs adaptation based on it. In contrast, embodiments disclosed herein use an effective mean mutual information (mean MI) metric. A different type of average MI metric has been used in classical approaches, however, the average MI metric in the present invention avoids the annoying but annoying correction necessary to improve performance in other FLA techniques such as MMIBM /calibration factor. Extensive and time-consuming simulations are required to obtain these correction/calibration factors, and the obtained correction/calibration factors do not properly cope with RF The role of the parity check (LDPC) encoder in the system is not so obvious.

The general steps of GP-based FLA can be summarized as follows:

Calculate the LQM of the received signal;

Input the calculated LQM and corresponding CRC results into the online learning algorithm of the GP system model to update the filter or model parameters of the GP system model;

Use the updated model parameters in the GP system model to generate BLER predictions for each considered CSI;

The BLER prediction is used to select the appropriate CSI to be returned to the transmitter.

An additional advantage of the GP-based approach described in the present invention compared to prior art methods is that free hyperparameters are obtained in a principled manner by evaluating marginal likelihoods.

For ease of description and understanding, an exemplary embodiment based on the 3GPP Terel-8 standard will be described here. In the given embodiment, the CSI selected as the feedback value is the CQI, which is sent to the transmitter for selection of the MCS. However, the methods and devices disclosed here are not limited thereto, and those skilled in the art can easily realize that other communication systems that provide methods for feeding back CSI from the transmitter to the receiver, such as WCDMA, WiFi, WiMax, and Other types of communication systems that may use other CSI, such as RI or PMI, can be modeled in a similar way and advantageously employ the methods and apparatus disclosed herein. Likewise, many of the terms used in the present invention have the same meaning as they are used in the LTE environment; however, it should be understood that other communication systems may use different terms to express similar concepts, and these systems can also benefit The embodiments disclosed in the present invention are adopted in an appropriate manner.

Referring now to FIG. 1, there can be seen a block diagram that incorporates aspects of the present invention and illustrates one embodiment of a receiver system 100 for an OFDMA communication system. The illustrated receiver system 100 receives a symbol stream 102 of OFDM symbols, which is separated into pilot symbols 110 and data symbols 109 by a pilot extractor 106 and a data extractor 104, respectively. Symbol stream 102 is received and digitized over a communication link, which may be a radio frequency link propagating through the air, or another type of suitable link or medium, before being forwarded to extractors 104 and 106 . The extracted pilot symbols 110 are provided to an estimator 108 which generates a channel estimate 111 and a noise covariance estimate 113 for subsequent calculations. Assuming perfect synchronization of time and frequency, under a given (LTE) resource element RE, the post-Fast Fourier Transform (FFT) received signal vector Y is shown in Equation (1):

Y=Hx+u, (1)

Y is a complex matrix An element of , NR is the number of receive antennas, Corresponding to the channel matrix, Indicates the number of spatial layers and NT is the number of transmit antennas. The resource element RE in the LTE system environment is the smallest time-frequency unit used to describe the physical downlink. Data is received on this link and corresponds to one OFDM symbol and one OFDM subcarrier. Unknown data symbols 109 and known pilot symbols 110 can be complex vector said, while is a complex additive white Gaussian noise (AWGN) vector. The channel estimate 111 and the noise covariance estimate 113 are generated by the estimator 108 after extracting the data 109 and pilot 110 symbol information accordingly. The illustrated receiver system 100 uses pilot symbol assisted channel estimation in an estimator 108 . Alternatively, other types of channel estimates may be used to obtain the channel estimate 111 and the noise variance estimate 113 . These estimated values 111 and 113 are provided together with the extracted data symbols 109 to a processing section 112 where the data symbols 109 are decoded and estimated information bits 118 are produced. Decoding is supported by control information 126 which is decoded and extracted from the control channel by the control channel process 122 . The generation of information bits 118 is done by MIMO detector 114 and turbo decoding 116 and creates estimated information bits 118 and associated CRC result 120 . The GP system model 124 is used to estimate CSI 130 possibly returned to the sender (not shown) for link adaptation. GP system model 124 receives CRC result 120 and other channel control information 128 from decoder 116 .

For example, in the illustrated embodiment, other channel control information 128 may include CQI/MCS used to encode information bits associated with CRC results. GP system model 124 may generate various CSIs, for example, in the illustrated embodiment of an LTE receiver, these CSIs 130 may include wideband-CQI, rank indication, subband CQI, wideband precoding matrix indication, and/or subband Precoding matrix indication. As will be discussed further below, the GP system model 124 generates BLER predictions to evaluate the performance of various link parameters and generates corresponding CSI 130 . CSI 130 can be sent back to a wireless base station or other wireless transmitter (not shown), where they can be used to adapt the RF link accordingly. Further, CSI 130 may be used in transmitter system 100 in connection with a receiver system (eg, when both the transmitter system and receiver system are part of or form one transceiver system).

In the exemplary embodiment using the LTE system to illustrate GP-based FLA, the CSI 130 chosen for illustration is a wideband-CQI, as specified by the LTE standard, with 29 available CQIs available for transmitting data to the UE A counterpart in MCS. Alternatively, other CSI 130 may be generated accordingly from the requested CSI report from the eNodeB (or generally from the base station) using a published GP system model based prediction technique.

FIG. 2 shows a flowchart of an embodiment of an exemplary method 200 for determining CSI including a GP system model for BLER prediction. Exemplary method 200 may be used to derive CQI values 220 or other CSI to provide closed-loop link adaptation in OFDMA or other types of communication systems. The channel estimate 111 and the noise covariance estimate 113, such as the channel and noise covariance estimates described with reference to FIG. The equalized SINR207 for the nth spatial layer and the considered RE is given by equation (2):

${\mathrm{<span\; class="notranslate">\; SINR</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; \&lsqb;</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; u</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&rsqb;</span>}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The notation A[) _{m, n} denotes the elements of the mth row and nth column of matrix A, where I is an identity matrix with appropriate dimensions.

An advantage of the GP technique disclosed in the present invention is that even if the receiver employs a non-linear equalizer such as an ML-type equalizer, the post-processing SINR value 207 can still be calculated using the LMMSE equalizer assumption. This is because the GP based LA feedback estimator is very insensitive to said type of equalizers in the system and is very well aware of the non-linear mapping from mean MI to CRC/BLER. Therefore, other information such as the ratio of data-to-pilot power is unnecessary.

The equalized SINR value 207 may be used to calculate 208 the LQM 209 . The LQM chosen in the disclosed embodiments is the mean MI metric because it has good properties based on information theory and has proven to be very stable through its use in the classical LUT-based LA method. In contrast, state-of-the-art LA methods use both average and ordered sets of post-processing SINR as LQM. These LQMs proved to be poor for both LUT-based and online learning-based LA methods. The average MI metric disclosed in the present invention does not require extensive simulations to obtain the correction/calibration factors needed to improve FLA performance for other LQMS like MMIBM. The calculation 208 of the average MILQM can be done in two steps. Computation 208 begins by estimating the MI 210 for each RE and each spatial layer (for a given rank assumption) for a given modulation alphabet used in a considered CQI/MCS on a considered RE. MI 213 can be estimated for each modulation alphabet using the computed post-processing SINR 207 . For example, as shown in Table 1, the estimation formula can be used for several modulation alphabets - quadrature phase shift keying (QPSK), 16-state quadrature amplitude modulation (16QAM) and 64-state QAM.

Table 1

The MI estimate 213 may be used to calculate 212 the average MI per codeword 209 for all layers within a codeword, and REs considered in a reporting subframe. A codeword is the result of a mapping, or channel coding, that maps a transport block or packet received from the Medium Access Control (MAC) layer into different codewords containing data bits and CRC bits. The codewords are then subjected to a process called modulation to generate a complex-valued OFDM baseband signal, which is then upconverted to the carrier frequency. Alternatively, in a non-OFDM type communication system, codewords may be prepared for transmission using a different modulation and upconversion scheme. In all of these schemes, each block of bits or codewords is converted into a data signal and then sent over a link to a receiver. As shown in equation (3), an arithmetic mean can be used to obtain a set of average MI209:

$\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}<span\; class="notranslate">\; )</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; E.</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; MI</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, γ is a normalization constant. In an alternative embodiment, the geometric mean may be used to calculate the set of mean MI 209 . The MI needs to be obtained for all modulation alphabets in the considered set of CQIs.

Prediction process 214 generates a set of BLER predictions for each CSI (in the particular embodiment shown in FIG. 2 , a CSI is a CQI) 211 using a set of average MIs 209 and CRC results 216 . As will be described in detail below, BLER prediction 214 can be accomplished by a set of GP system models, where each CQI index has its own GP system model. In some embodiments, all GP system models may have the same processing steps, but training data dictionaries and/or model parameters may differ. These GP system models have two working modes: training mode and prediction mode. In prediction mode, each GP system model for each CQI index produces a predicted BLER based on a set of estimated mean MI 209 in the current subframe for the CQI considered. In training mode, the corresponding GP system model for each CQI index is trained and updated with the corresponding buffered average MI calculated in the previous subframe according to the availability of CRC results for each CQI. Only received codewords have accurate CRC results, therefore, for each set of received data, only one GP system model corresponding to the received CQI can be updated. This way, training will be slightly slower after UE restarts or long periods of discontinuous reception.

To speed up several GP system model training for different CQI indices from a set of received data, one CRC result can be estimated for CQIs other than the CQI of the currently received codeword. When the CRC result of the received CQI is pass, all the CRC results of the lower CQI, ie the CQI corresponding to the lower throughput MCS, may also assume that the CRC result is pass. Conversely, when the CRC result of the currently received CQI is failure, all CRC results of higher CQIs, that is, CQIs corresponding to higher throughput MCSs, may also be assumed to be failures. All GP system models correspond to the current CQI and higher or lower CQIs according to the above CRC assumption rules. For simplicity, it can be assumed that, in the case of HARQ retransmission, the same CQI index is used in the retransmission as in the initial transmission.

In some embodiments, Outer Loop Link Adaptation (OLLA) may be included to help GP-based FLA learn faster. This OLLA can be considered for receiver and/or transmitter.

The CQI 220 is selected 218 as an output or result of the method 200 by identifying the highest throughput CQI (i.e., the CQI corresponding to the MCS with the greatest throughput) such that the predicted BLER for the selected CQI 220 is less than or equal to the predetermined BLER The threshold is, for example, a BLER of about 0.1. It is proposed again that, also in this exemplary embodiment, the generated CSI value is CQI, and according to further embodiments, other types of CSI values may also be generated through the method 200 . The generated CQI 220 can be used for fast link adaptation (that is, to select the MCS corresponding to the CQI 220).

Figure 3 shows the application 300 of the training mode 302 and the prediction mode 304 of the GP system model for the prediction of BLER estimates 314 for selection of a wideband CQI value. Prediction mode 304 receives LQM 312, which in some embodiments may be the average MI value per codeword for the currently received codeword, and generates BLER prediction 314 using a set of model parameters 306 computed by training process 302, before selecting a recommended The wideband CQI is used. Each computation interval or iteration may be periodic, e.g., corresponding to each received subframe, frame, or other periodic unit of received data; or, the iteration may be aperiodic, e.g., upon request of the transmitter to report CSI.

The training mode 302 receives the LQM 308 from the previous computation interval and the CRC result 310 from the current computation interval, and updates 306 the set of model parameters. The time taken for calculation, selection, and transmission of CQI is limited. For example, it may take about 8 milliseconds to calculate, select, and send a recommended CQI value to the transmitter. The transmitter will spend extra time adjusting system parameters and sending data to the receiver. In an LTE system, the delay of the transmitter may be subframe time or about 1 millisecond. Therefore, between receiving a set of data, selecting a new CQI, and receiving a CRC result based on the data transmitted using the brand new CQI, there is a delay, eg, about 9 milliseconds in the above example. To account for this in the GP system model, the training pattern 302 uses a time-delayed LQM 308, where the LQM 308 may in some embodiments be a set of average MIs, and the CQI is generated from the LQM308 of the time delay. The term link quality metric (LQM) is used interchangeably in this disclosure to refer both to a metric, ie a function, and a value calculated using the metric. The delayed LQMs may be referred to as a set of cached LQMs, which may be stored in a computer memory called a buffer and retrieved at a later time. In some embodiments, hybrid automatic repeat request (HARQ) may be used. In embodiments employing HARQ, the UE may assume that each retried packet is encoded based on the CQI of the original transmission resulting in greater latency and additional buffering.

To help understanding, it is helpful to consider a specific example, for example, a 4×4 MIMOLTE system with a cell bandwidth of 20 MHz and a maximum of 100 Physical Resource Blocks (PRBs). Please note that the specific examples given here are only to aid in understanding and should not be construed as limiting the invention in any way. In a typical LTE system, there are generally 15 supported CQIs. It is worth noting that LTE supports multiple block sizes. It is well known that the largest code block provides better BLER performance than the smallest code block. Therefore, the performance of different code block sizes (or allocated PRBs) needs to be considered when selecting the CSI, such as CQI/PMI/RI, to be reported back to the transmitter.

When selecting the feedback value of CSI, a separate GP system model is used for each combination of CQI and code block size, so a large number of GP system models need to be maintained. To reduce the number of GP system models, a subset of possible code block sizes can be used. For example, in a system with a bandwidth of 20 MHz, with a maximum of 100 PRBs, the selected subset may contain a reduced number, e.g., 3 code block sizes, or the number of PRBs, corresponding to, e.g., 6 PRBs , 50 PRBs, and 100 PRBs. After reduction, there are only 3 code block sizes and 15 supported CQIs, which can support subband and wideband CQI feedback at the same time; a 15×3 or forty-five (45) GP system model is adopted. In training mode, if the allocated bandwidth in the current received subframe has 12 PRBs, the CRC result can be used to train the GP system model corresponding to the bandwidth used; in the current example, it is associated with 6 PRBs 15 GP system models. Similarly, if the allocated bandwidth in the next subframe is 38 PRBs, 15 GP system models associated with 50 PRBs (corresponding to 15 supported CQI ). In the present example, a broadband GP system model is assumed to be associated with a GP system model of 100 PRBs. In predictive mode, the receiver computes the wideband and a set of subband LQMs simultaneously, then uses the respective GP system models to predict the BLER.

When selecting PMI/RI feedback values in an LTE system example as described above, each rank assumption has a set of GP system models, and there are 3 (bandwidth) × 15 (supported CQI) × 4 (rank assumptions), that is, 180 A GP system model. The intended complexity cost of GPFLA is mainly determined by the viewport or dictionary size. With a dictionary size of about 3 to 5, a typical receiver can easily handle the typical implementation cost of 180 GP system models. For the option of PMI feedback, the receiver can implement 180 GP system models for each PMI, or alternatively, can first determine a suitable PMI from LQM without GP system, thus simplifying the system.

The GP system model is based on a kernel function that implicitly maps low-dimensional input data to a high-dimensional output data for performing and utilizing linear functions for regression and classification. This mapping can be viewed as a distribution over a function. The free hyperparameters associated with the GP system model can be obtained or learned by maximizing the marginal likelihood. Often this is more efficient than performing a standard grid search over many free parameters.

In one embodiment, the GP-based FLA method includes a non-recursive or sliding window GP system model to determine the channel quality information fed back to the transmitter. A non-recursive or sliding window GP system model uses a dictionary containing training data corresponding to data collected at time intervals or windows, where the window slides forward in time over time. Continuing with the LTE example of candidate CQIs for codewords, there will be a finite number of M pairs of training data in the dictionary or window, where each pair includes the average MI, and the corresponding CRC result and CQI value.

A non-recursive or sliding window GP system model, as one possible implementation of the GP system model 124, can be used in step 214 of the method 200 to select a CQI in two stages:

The first stage calculates the effective/average MI for each codeword corresponding to wideband or subband CQI;

The second phase consists of a training step and a prediction step:

a. At training/update time, when a given CQI has a CRC result, the CRC result including the corresponding (delayed) average MI in a considered modulation alphabet for the CQI candidate is passed to the non-recursive GP System model to calculate filter coefficients, average MI/CQI/CRC data is used to update dictionary.

b. In prediction, the filter coefficients are used together with the current mean MI value to predict the BLER value for each considered CQI/MCS.

Note that the average MI/CRC of pairs of input/output within a window are cached, i.e. stored in memory, for later retrieval, for training or calculation of model parameters, as well as for BLER prediction modes. However, if the CRC result is available for the CQI or has been estimated as described above, the training mode is only active for the considered CQI.

A set of mean MI input/output data pairs and contained in The corresponding delayed CRC result in the dictionary can be expressed by equation (4):

Where: mMI _i corresponds to the mean MI at the i-th instance or index in the dictionary; CRC _i corresponds to the CRC result at the i-th instance or index in the dictionary; M is an integer value representing the size of the dictionary. It should be noted that in the dictionary A set of input-output pairs in does not need to be continuous in terms of time or subframes; the i-th index may simply represent an index identifying the data pair in the dictionary. The regression or (non-linear) mapping from mean MImM to CRC (or equivalent BLER) can be described by equation (5):

where f(.), is a latent or unknown function that maps the input mean MI to the CRC output; w is a column vector of weights for the linear regression model; corresponds to the feature space; ε corresponds to being modeled as having zero mean and variance The model error of the independent and identically distributed (IID) Gaussian noise of , where

For FLA, it is necessary to predict the CQI candidates given by the current set based on the training data Calculated (ie, current subframe or time interval) average MI to generate CRC/BLER results. For simplicity, let the set of training data (for brevity, can be marked without superscript case) the set of input data is represented as a vector of real numbers (assuming t < M), the CRC result of the group is represented as a vector of binary values, in, The likelihood of the weights can be described by Equation (6):

Thus, the weighted likelihood fit has an average and variance Gaussian distribution, that is,

Assuming the prior distribution of weights is with zero mean and covariance matrix Σ, Gaussian distribution of , the posterior distribution of weights is given by equation (7):

Equation (7) can be rewritten as Equation (8):

in, Therefore, for convenience, the posterior distribution of weights can be expressed by Equation (9):

in, and This shows that the predicted distribution of the currently computed mean MImMI _t over the CRC results can be obtained by averaging all possible linear model outputs over the posterior distribution of weights as shown in Equation (10).

By the matrix inversion lemma and applying the so-called kernel trick to obtain the predicted mean shown in equation (11) and the covariance shown in equation (12), the predicted distribution shown in equation (10) can be rewritten as:

in, is a vector, by computing the kernel function element-wise, combining dictionaries All input data in to describe the similarity of the currently available input data mMI _t .

For example, a Gaussian kernel, also known as a radial basis function (RBF), is expressed as

$\mathrm{<span\; class="notranslate">\; \&kappa;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

where l is called the kernel width and is a free parameter (needs to be tuned, or can be obtained from a given dictionary automatically obtained in ) including the variance σε2. Similarly, is the covariance matrix obtained by computing the kernel function for each combination of a given set of input and output data. The values α _i are typically time-varying filter coefficients.

The non-recursive GP system model discussed above requires online matrix inversion (Equation 11), which is computationally very expensive for practical systems, especially for larger window sizes. Alternatively, a recursive GP system model can be used for FLA. One such recursive GP system model may be called Kernel Recursive Least Squares with Tracking, KRLS–T. The full or non-recursive GP system model described above can be re-formulated in a recursive form.

like and Equation (11) and equation (12) can be rewritten as:

$\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&kappa;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

Considering the linear model shown in equation (5) for mapping the mean MI to the CRC estimate (or equivalently the BLER estimate), the predicted distribution of CRC can be obtained using equations (13) and (14) , as shown in equation (15):

To obtain a recursive GP system model for CRC/BLER prediction, in Predicted mean (μ _{f( )} ) and covariance of up to (t-1)-th sample data in the group Respectively shown in equation (16) and equation (17);

${\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \}</span>}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

When new data are available in training mode (mMI _t , CRC _t ), then the recursive update of the mean and covariance is given by Equation (18) and Equation (19), respectively:

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; CRC</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; CRC</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& {\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; CRC</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& {\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

in, $h_t={\mathrm{\&Sigma;}}_{t-1}{K}_{t-1}^{-1}{k}_t=(I-K_{t-1}{C}_{t-1}^{-1})k_t.$

At the next update, new data (mMI _t+1 , CRC _t+1 ) will be available, thereby increasing the size of the matrix. Update to previous matrix by using rank-1 As shown in equation (20), large and growing matrices can be avoided Online inversion of :

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]{\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

Wherein, q _t =Q _t-1 k _t .

In the above derivation, two factors were neglected: a useful forgetting factor λ∈(0,1] in a non-stationary environment; and the size limit of the codebook and dictionary, that is, the need to limit the The amount of data in to help with implementation.

The recursive GP based CRC/BLER prediction (including training and prediction modes), i.e. the KRLS–T algorithm, can be summarized as follows using the mean MI and CRC results (if available). First, an initialization step is performed using an initial set of mean MI, mMI ₀ , and the CRC result from the first iteration, CRC ₁ , as described above, the mean MI is cached or delayed, marked for use with CRC ₁ mMI ₀ , .

The initial filter coefficients are calculated using Equations 7a, 7b, 7c and 7d:

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&rsqb;</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; CRC</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>$

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\\ {\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; \&rsqb;</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>$

Q ₀ =[K(mMI ₀ , mMI ₀ )] ⁻¹ , (7c)

X = {mMI ₀ }. (7d)

Among them, σε2 represents a modeling error, and K(·,·) represents a kernel function as described above. At each time iteration, the BLER prediction denoted by subscript t is obtained and covariance σyt2 for each input/output pair in the training data dictionary, where M denotes the number of input/output pairs in the dictionary. The input in each pair is the delayed average MI for a given subframe, and the output is the corresponding CRC result. Each pair is denoted by subscript i, where i=0, 1, 2, . . . M. In each iteration t (defined as t=i+1), for each average MI/CRC pair i, the following algorithm can be used to obtain a prediction.

The current filter parameters are updated as shown in Equations 8a and 8b:

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&LeftArrow;</span>\sqrt{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>$

Σ _i ← λΣ _i + (1-λ)K(X,X), (8b)

where λ∈0(1]) is the forgetting factor, which is an additional free parameter of the KRLS-T algorithm. Next, evaluate some intermediate values using equations 9a, 9b, 9c, and 9d:

q _t =Q _i K(mMI _t ,X), (9a)

h _t =Σ _i q _t , (9b)

${\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; MMI</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span>$

The BLER predicts and covariance σyt2 or uncertainty can be obtained by Equations 10a and 10b:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>$

Then, update the filter parameters for the next iteration using Equations 11a, 11b, and 11c:

${\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ {{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& {\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ {\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]{\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ {\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]{\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>$

Then, the input vector X is updated using the mean MImMI _t , as shown in Equation 12:

X = {X, mMI _t }. (12)

The advantages of the above-described GP system model FLA technology embodiment can be seen by performing simulations in a 3GPP LTE Terel-8 system using closed-loop link adaptation to select CQI feedback and adjust the transmitter's MCS. The simulation runs were performed to compare the recursive GP based FLA embodiment, KRLS-T as described above, with the QKLMS based method and the traditional or classical MMIBM method. The simulation parameters used in each run are listed in Table 2 below.

Table 2

Fig. 4 shows a graph 400 of the total throughput of the physical downlink shared channel PDSCH with frequency division duplexing FDD. In FIG. 4 , the vertical axis 402 represents the total throughput of two codewords in megabits per second (Mbps), and the horizontal axis 404 represents the signal-to-noise ratio (SNR) in decibels db. FIG. 5 shows a graph 500 of the average BLER for two codewords obtained for the simulation in FIG. 4 using the same simulation parameters as in Table 2. In FIG. 5 , the vertical axis 502 represents the average BLER of two codewords in percentage, and the horizontal axis 504 represents the signal-to-noise ratio (SNR) in decibels db.

Table 3 provides a description of the graph labels shown in the legends of Figures 4 and 5.

table 3

The graph 400 shows that the disclosed recursive GP-based FLA, KRLS-T, can outperform the classical MMIBM method in terms of throughput, and the graph 500 shows that the recursive GP system model, KRLS-T, compares favorably with the classical MMIBM-based method. than, have a better performance in keeping the average BLER below the desired threshold of 10%. It is also evident from Fig. 4 that the Quantized Kernel Least Mean Square, QKLMS, LA approach provides similar performance to GP-based FLA in terms of throughput and BLER.

It is not surprising that the QKLMS method provides similar performance. Because, it is well known that QKLMS based FLAs can perform very well once properly tuned. However, QKLMS cannot adapt or track changes as quickly as possible to perform well on the ever-changing wireless medium. Fig. 6 shows the tracking performance curves 600 and 601 of the new recursive GP system model FLAKRLS-T compared with the tracking performance of the previous QKLMSLA method. Graph 600 shows the tracking performance of the LA method based on QKLMS and the new recursive GP-based FLA method KRLS-T, the throughput of zero codewords in Mbps is shown on the vertical axis 602, and the throughput of zero codewords is shown on the horizontal axis 604 shows the number of subframes sent. The graph 601 shows both the instantaneous throughput difference on the vertical axis 606 and the number of transmitted subframes on the horizontal axis 604 for QKLMS and KRLS-T techniques. Graphs 600 and 601 show that the recursive GP-based FLA converges to average throughput much faster than the QKLMS-based method. It can be seen that, compared with the link adaptation method in the prior art, the FLA method of the GP system model disclosed in the present invention performs better and can track changes in the link medium faster.

FIG. 7 is a block diagram showing a wireless communication device 700 suitable for performing the FLA method described in the present invention. Apparatus 700 includes processing means 702 coupled to computer memory 704 , a radio frequency (RF) unit 706 , a user interface (UI) unit 708 , and a display unit 710 . In some embodiments, no user interaction is required. In these embodiments, user interface 708 and display 710 may be omitted from device 700 . Apparatus 700 can be used in various forms of MSs of wireless communication UEs, such as mobile phones, smart phones, tablet devices and the like. The processing device 702 may be a single processing device, or may include multiple processing devices, including dedicated devices, such as digital signal processing (DSP) devices, microprocessors or other specialized processing devices, and general-purpose processors.

Memory 704 is coupled to processing device 702 and may be a combination of various computer memories, such as volatile memory, nonvolatile memory, read-only memory (ROM), or other types of computer memory, storing computer program instructions, instruction It may constitute a method group including operating system, application, and file system, and may also be other computer program instructions for other ideal computer-implemented methods, for example, the FLA method disclosed in the present invention. Memory 704 also includes program data and data files, which are stored and processed by computer program instructions.

A radio frequency (RF) unit 706 is coupled to the processor for receiving and/or transmitting radio frequency signals based on the digital data 712 exchanged with the processing device 702 . RF unit 706 includes an analog-to-digital converter for digitizing the received RF signal at a desired sampling rate, for example, 30.72 megahertz (MHz) sampling rate is typically used for an LTE channel bandwidth of 20 MHz, and then transmitting the digitized RF signal 712 to processing device 702 . Conversely, the RF unit 706 may include a digital-to-analog converter for converting digital data 712 received by the RF unit 706 from the processing device 702 into analog signals for transmission.

UI 708 may include one or more well-known user interface elements, such as touch screens, keys, buttons, and other elements for exchanging data with the user. The display 710 is used to display various information suitable for the UE, and may be implemented by any well-known display type, for example, an organic light emitting diode (OLED), a liquid crystal display (LCD), and the like. The communication device 700 is suitable for executing the FLA method and algorithm described in the present invention with reference to FIG. 1 and FIG. 2 .

Therefore, while there has been shown, described and indicated herein the essential novel features of this invention as applied to the exemplary embodiments thereof, it should be understood that those skilled in the art can make further changes without departing from the spirit and scope of the invention. Various omissions, substitutions and changes are made in the form and details of the apparatus and methods, and the operation of the apparatus. Furthermore, it is expressly intended that all combinations of those elements which perform substantially the same function in substantially the same way to achieve the same results are within the scope of the invention. Furthermore, it should be recognized that structures and/or elements shown and/or described in connection with any form or embodiment of the invention disclosed may be incorporated as a general item of design choice into any other form or embodiment disclosed or described or suggested. Examples. Accordingly, the invention is to be limited only by the scope described in the appended claims.

Claims (15)

1. A transceiver (700) for selecting channel state information (CSI) of a communication link, characterized in that, the transceiver (700) comprises: a receiver (706) for receiving a communication signal (102) from said communication link and generating a received data signal; processing means (702), coupled to said receiver (706), for receiving said data signal; a memory (704), coupled to said processing means (702), Wherein, the processing device (702) is used for: Based on the received data signal (102), generate a channel estimate (111), a noise covariance estimate (113) and a set of cyclic redundancy check (CRC) results (120); Generate a set of link quality metrics (LQM) (209) based on the channel estimate (111) and the noise covariance estimate (113); Caching the generated set of LQMs (209); updating model parameters of a GP system model (302) using a Gaussian process (GP) system model based on said cached set of LQMs (209) and said set of CRC results (120); Based on the generated set of LQMs (209), the block error rate (BLER) is predicted (124), (214), (304) for each CSI in the set of supported CSIs using the updated model parameters and the GP system model (211); From the set of supported CSIs is selected (210) a CSI (220) with a maximum throughput and a predicted BLER below a threshold. 2. The transceiver (700) according to claim 1, characterized in that, using the GP system model to update model parameters comprises: Based on the generated set of CRC results (120), the cached set of LQM (209) and training data dictionary, update model parameters; The training data dictionary is updated based on the cached set of LQMs (209), generated CRC results (120) and the CSI of the received data signal. 3. The transceiver (700) of claim 2, wherein the training data dictionary comprises sets of cached LQMs, at least one set of CRC results associated with each set of LQMs, and an associated set of CSIs. 4. The transceiver (700) according to claim 3, wherein the training data dictionary is enhanced by: When the CRC result generated for the current CSI is passed, all low-throughput CSIs in the supported set of CSIs are associated with the CRC passed result; When the CRC result generated for the current CSI is pass, all low-throughput CSIs in the supported set of CSIs are associated with the CRC pass result. 5. The transceiver (700) according to any one of claims 1 to 4, characterized in that the GP system model is a non-recursive GP system model. 6. The transceiver (700) according to claims 1 to 4, characterized in that the GP system model is a recursive system model. 7. The transceiver (700) according to any one of claims 1 to 6, characterized in that the LQM (209) is an effective mean mutual information (mean MI) metric. 8. The transceiver (700) of claim 7, wherein generating a set of average MIs comprises: Based on the assumption of a linear equalizer, and the received data signal is adjusted by nonlinear equalization, generating mutual information (MI) values for each RE in the received data signal; Based on the generated MI values, the set of valid average MIs is generated. 9. The transceiver (700) according to claim 5 or 6, wherein the GP system model comprises a group of GP system models, wherein: Each GP system model in the set of GP system models is used to predict a BLER for a particular CSI; When the CSI associated with the received data signal is not associated with any of the set of GP system models, the GP system model associated with the most recent CSI is updated. 10. The transceiver (700) according to any one of claims 1 to 9, wherein the CSI value is a wideband channel quality indicator (CQI), subband CQI, rank indication, wideband precoding Matrix indication (PMI), or subband PMI. 11. The transceiver (700) according to any one of the preceding claims 1 to 10, characterized in that said communication link comprises a wireless communication link and said receiver comprises a Radio Frequency (RF) unit. 12. The transceiver (700) according to any one of the preceding claims 1 to 11, characterized in that said communication link comprises a communication link of Orthogonal Frequency Division Multiple Access (OFDMA) type. 13. The transceiver (700) according to claim 12, characterized in that said system comprises nonlinear equalization or linear equalization. 14. The transceiver (700) according to any one of claims 11 to 13, characterized in that said system is a user equipment comprising a user interface (708) and a display (710). 15. A computer program product comprising a non-transitory computer-readable storage medium storing data which, when accessed by a processing means, performs operations comprising: Receive channel estimate (111) and noise covariance estimate (113); Generate a set of link quality metrics (LQM) (209) based on the channel estimate (111) and the noise covariance estimate (113); Caching the generated set of LQMs (209); generating a set of cyclic redundancy check (CRC) results (120) based on the received data signal (102); updating model parameters of a GP system model (302) using a Gaussian process (GP) system model based on said cached set of LQMs (209) and said set of CRC results (120); Based on the generated set of LQMs, each CSI prediction (124), (214), (304), block error rate (BLER) (211) in the set of CSIs supported by the updated model parameters and the GP system model is used ; From the supported set of CSIs, the CSI with maximum throughput (220) and predicted BLER below a threshold is selected (210).